In X-ray computed tomography a "slice" of an object is presented as an image on an imaging device, where the imaging device may be a cathode ray tube, a television screen, a plotter, etc. The image is created by first measuring the X-ray transmission of the object using "pencil" X-ray beams along many substantially parallel paths, for example 256 parallel pencil paths. Secondly, the orientation of the parallel paths is rotated through a small angle and the transmission measurements are repeated. Typically, a set of parallel X-ray transmission measurements are made at every one degree of rotation for each of the 180 degrees of a half circle. In this example, there will be 256 parallel measurements of X-ray transmission for each of 180 degrees, to give a total of 46,080 transmission measurements. Thirdly, a computer then uses this large number of X-ray transmission measurements in order to compute the X-ray attenuation coefficients in each volume element of the slice. A volume element of the slice will hereinafter be referred to as "voxel". The values of the X-ray attenuation coefficients are then converted to a set of "gray scale" values, and the gray scale values are presented as the image on the imaging device.
The image presented on the imaging device, such as a television screen or a plotter, are presented as "pixels". The two dimensional image is made of rows and columns of pixels, each pixel is represented by a digital number, and the digital number controls the display presented in the pixel.
A pixel represents the image of a voxel. The voxel is the three dimensional box within the object to be imaged, such as a patient, and the voxel contains materials of the object. The contents of the voxel are computed by an image reconstruction calculation, and are obtained as a number representing the X-ray attenuation of the material contained within the voxel. The number is then used to control the display presented in the pixel.
Many variations in making the X-ray transmission measurements have been used. For example, fan beam geometries have been employed rather than parallel beam geometries. A fan beam is produced by having one X-ray tube, and having many pencil beams collimated from this X-ray tube. A separate detector is installed for each pencil beam of the fan beam. The X-ray tube, collimators, and detectors are all mounted on a rotatable gantry so that the assembly may be rotated relative to the object, such as a patient. In a fan beam, the X-ray pencil beams make a small angle to each other, rather than follow parallel paths. The fan beam is used for transmission measurements at one orientation, and then the entire fan beam is rotated relative to the object, and in the plane of the desired slice, in order to produce another set of X-ray transmission measurements. The image of the slice is then reconstructed from the set of fan beam measurements made at each of the rotation angles.
The pencil X-ray beams naturally diverge, rather than maintain a parallel pencil structure. Divergence of the individual pencil beams may be accounted for in the image reconstruction process. For example, transmission measurements may be made at each angle through a rotation of 360 degrees, and oppositely directed measurements may be averaged together in order to account for divergence of the pencil beams.
Further, the object may be moved along the axis of the gantry in order to rapidly obtain transmission measurements for several parallel slices. Continuous motion of the object along the axis of the gantry causes the transmission measurements to produce a spiral pattern within the object, but still the X-ray transmission coefficient of a voxel may be computed by the computer.
Various difficulties arise in the computation of the X-ray transmission coefficient for a voxel. One difficulty arises from the fact that the X-ray attenuation coefficient of a material depends upon the atomic number of each element comprising the material, and also upon the density of the material. For example, water is made of hydrogen and oxygen, and tissue is made of hydrocarbon molecules which are principally made of hydrogen, carbon, and oxygen. In contrast, bone has a large component of calcium. Bone, accordingly, is made of materials having higher atomic number than soft tissue or water. Further, bone is considerably more dense than soft tissue or water. Accordingly, bone has a significantly higher attenuation coefficient for X-ray photons ordinarily used in X-ray tomography.
A difficulty in reconstructing the image from the X-ray transmission measurements arises in imaging a slice of a patient, where the slice contains both bone and soft tissue. It is usually desired to reconstruct an image of the soft tissue. For example, when it is desired to image a patient's brain, a slice of the patient's head is imaged. The head consists of a skull made of dense bone containing calcium, and a brain made of soft tissue composed of mainly water and hydrocarbons. Accordingly, the dense, calcium containing, skull has a significantly higher X-ray attenuation coefficient than does the soft tissue brain.
An artifact is introduced into the computation of the X-ray attenuation coefficient of each voxel by the "partial volume" effect. The partial volume effect is the effect on image reconstruction produced by a voxel containing two different materials, where the two different materials have different X-ray attenuation coefficients. For example, in imaging a patient's head, a voxel may contain both skull and soft tissue. A voxel near the brain-skull interface will contain both skull and soft tissue.
In imaging a patient's brain, a transmission measurement will contain bone at both the point where the X-ray beam enters the head, and also where the X-ray beam exits the head. As a result, the reconstructed X-ray density along the line of the X-ray beam may be erroneously high, leading to a streak in the image. This streak effect is particularly troublesome in image regions where the amount of bone in neighbor voxels changes along the line of the X-ray pencil beam. For example, curvature of the skull in a plane perpendicular to the plane of the slice may cause varying amounts of bone to project into voxels lying along a line of an X-ray pencil beam.
A particularly disadvantageous result of the partial volume effect is that the reconstructed image contains streak artifacts. Further, the value of X-ray attenuation coefficient computed in a voxel will depend upon a number of extraneous factors such as the partial volumes of neighbor voxels. For example, in imaging a patient's head, a number of the X-ray pencil beams may be substantially tangent to the interface between the skull and the brain, resulting in a line of voxels having rather large partial volume effects. Further, an X-ray pencil beam perpendicular to the skull and passing through the same voxel as the tangent pencil beam will have only a few voxels exhibiting a partial volume effect. The ordinary computational procedure for reconstructing the image cannot properly handle this variety of partial volume effects.
Previous methods of correcting a CT image for volume average effects have included simply lumping the run length of volume averaged voxels together into a combined voxel, and computing a correction X-ray attenuation coefficient for the combined voxel. The paper by D. J. Goodenough, K. E. Weaver, H. Costaridou, H. Erdmans, and P. Huysmans, "A New Software Correction Approach to Volume Averaging Artifacts in CT", published in "Computerized Radiology", Vol. 10, Nos. 2/3, Pages 87-98, 1986, discloses combining the voxels of the run length of volume averaged voxels into an effective voxel.
A further previous method looks at the slice above and the slice below the slice of interest, and establishes an order for three sublayers in the slice of interest in accordance with the values of X-ray attenuation coefficient calculated in the upper slice and the lower slice during the original reconstruction of the image. Values of X-ray attenuation coefficient are then assigned to the three sublayers in the slice of interest by interpolating the values of X-ray attenuation coefficient given for the slice above and the slice below. This method is disclosed in the paper by G. H. Glover and N. J. Pelc, "Nonlinear Partial Volume Artifacts in X-ray Computed Tomography", "Medical Physics", 7(3), pages 238-248 (May/June 1980).
There is needed a method to reconstruct an image from X-ray transmission measurements which will reduce artifacts arising from an interface in the object being imaged, where the interface is formed by two materials having different X-ray absorption characteristics. In particular, there is needed a method for reconstructing images having an interface between bone and soft tissue.